A necessary and sufficient condition for C 1 -regularity of solutions of one-dimensional variational obstacle problems
Mandallena, Jean-Philippe1
1 Université de Nîmes, France
Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 103-134.
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In this paper we study the C 1 -regularity of solutions of one-dimensional variational obstacle problems in W 1,1 when the obstacles are C 1,σ and the Lagrangian is locally Hölder continuous and globally elliptic. In this framework, we prove that the solutions of one-dimensional variational obstacle problems are C 1 for all boundary data if and only if the value function is Lipschitz continuous at all boundary data.

Publié le :
DOI : 10.4171/RSMUP/33
Classification : 49, 00
Mots-clés : One-dimensional variational obstacle problems, $C^1$-regularity, value function, conditional equa-continuity.
Mandallena, Jean-Philippe 1

1 Université de Nîmes, France 
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     author = {Mandallena, Jean-Philippe},
     title = {A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {103--134},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {142},
     year = {2019},
     doi = {10.4171/RSMUP/33},
     mrnumber = {4032807},
     zbl = {1439.49002},
     url = {http://archive.numdam.org/articles/10.4171/RSMUP/33/}
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Mandallena, Jean-Philippe. A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems. Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 103-134. doi : 10.4171/RSMUP/33. http://archive.numdam.org/articles/10.4171/RSMUP/33/

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